2007/11/25 by Mattia Cafasso, M. Cafasso · 9 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Block (permutation group theory) #Class (philosophy) #Connection (principal bundle) #Grassmannian #Holomorphic and Operator Theory #Integrable system #Limit (mathematics) #Manifold (fluid mechanics) #Point (geometry) #Toeplitz matrix #math-ph #math.FA #math.MP #msc:37K10 #msc:47B35 #nlin.SI
paper · pdf · doi:10.1007/s11040-008-9038-7
published in Mathematical Physics Analysis and Geometry 11(1), 11-51 (Springer Science+Business Media) · 35 pages. Typos corrected, some changes in the introduction
arxiv created 2007/11/25 · openalex publication_date 2008/02/01 · arxiv updated 2013/06/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We propose a method for computing any Gelfand-Dickey tau function living in Segal-Wilson Grassmannian as the asymptotics of block Toeplitz determinant associated to a certain class of symbols. Also truncated block Toeplitz determinants associated to the same symbols are shown to be tau function for rational reductions of KP. Connection with Riemann-Hilbert problems is investigated both from the point of view of integrable systems and block Toeplitz operator theory. Examples of applications to algebro-geometric solutions are given.